How do I make this twisted surface on a bottle?
I would do it this way:


Create a plane, rotate it 90° on the X axis, apply the rotation, mirror it, create your slot.
Give it an Array modifier with a Count of 8, enable the Merge option.
Give it a SimpleDeform modifier / Bend mode, with an Angle of 360°. Now it's a cylinder.
To make it twist give it a SimpleDeform modifier / Twist mode, create an empty to give it a correct origin and choose it as the Axis, Origin. Choose your Deform Angle (probably 180° and not 120° though).
Now, as you want the shape to reduce at its top, and as a simple scale with Proportional Editing risks to mess up your topology, you should use a Lattice: Create a Lattice that contains your object, subdivide it in the Properties panel > Data > Lattice, then in the same panel > Shape Keys, create 2 shapekeys, one basic, and a second that you will model in Edit mode.
Back in Object mode, give your object a Lattice modifier, select the lattice you've created as Object, select the lattice and in the Properties panel > Data > Shape Keys, put second shapekey at a value of 1. Now your object will deform according to the lattice second shapekey.
Give your object a Subsurf modifier, press Shading > Smooth in the Tools panel of the 3D view.
Once you're glad with the shape, apply all the modifiers except the Subsurf, go in Edit mode and remove the doubles to join at the 360° junction.